Geodesic
A Hybrid High-Order method for Kirchhoff–Love plate bending problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 393-421

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We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff–Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree  k ⩾ 1 are used as unknowns, we prove convergence in  h k + 1 (with  h denoting, as usual, the meshsize) in an energy-like norm. A key ingredient in the proof are novel approximation results for the energy projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in  h k + 3 is also derived for the L 2 -norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization.

DOI : 10.1051/m2an/2017065
Classification : 65N30, 65N12, 74K20
Keywords: Hybrid High-Order methods, Kirchhoff–Love plates, biharmonic problems, energy projector

Bonaldi, Francesco 1 ; Di Pietro, Daniele A. 1 ; Geymonat, Giuseppe 1 ; Krasucki, Françoise 1

1 
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     author = {Bonaldi, Francesco and Di Pietro, Daniele A. and Geymonat, Giuseppe and Krasucki, Fran\c{c}oise},
     title = {A {Hybrid} {High-Order} method for {Kirchhoff{\textendash}Love} plate bending problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {393--421},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {2},
     year = {2018},
     doi = {10.1051/m2an/2017065},
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     mrnumber = {3834430},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017065/}
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Bonaldi, Francesco; Di Pietro, Daniele A.; Geymonat, Giuseppe; Krasucki, Françoise. A Hybrid High-Order method for Kirchhoff–Love plate bending problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 393-421. doi: 10.1051/m2an/2017065

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